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Week1.3ConstructionMath.pdf

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Good or bad design?

Week 1.3

Construction Math

and Application

Objectives

▪ Convert between improper

fractions and mixed

numbers.

▪ Add, subtract, multiply,

and divide decimal

fractions.

▪ Calculate dimensions.

▪ Calculate areas and

volumes of objects.

▪ Relate math to construction

problems.

Countries That Do Not Use the Metric System

▪ Real reason USA does not use the metric

system

Fractions

(Goodheart-Willcox Publisher)

Proper Fractions

▪ Numerator is less than the denominator

Improper Fractions

▪ Numerator is greater than the denominator

Good or bad design?

Using Fractions

▪ Whole numbers can be changed to fractions

▪ Example:

• Change the whole number 6 into fourths

6 =

Using Fractions

▪ Mixed numbers can be changed into improper

fractions

▪ Example:

• Convert 3 5/8 to an improper fraction

5 3 =+=+



  

 =

Using Fractions

▪ Improper fractions can be reduced to a whole or

mixed number

▪ Example:

• Reduce 17/4 to the lowest proper fraction

1 4417

17 ==

Using Fractions

▪ Reduce fractions by dividing numerator and

denominator by the same number

▪ Example:

• Reduce 6/8 to the lowest fractional form

6 =



 =

Good or bad design?

Adding Fractions

▪ All denominators must be the same

▪ Find the least common denominator (LCD)

▪ Add the numerators

▪ Convert to a mixed number

Adding Fractions

▪ What is the least common denominator?

• Example:

• What must you multiply to get a common

denominator?

=++ 32

5 =

3 =

Adding Fractions

▪ Example:

▪ Add and convert to a mixed number

=++ 32

1 1

10 ==++

Adding Fractions

Take 15 minutes to complete the

Practice Problems in the textbook.

Practice Problems Answer Key

1. 1 3/8

2. 1 1/16

3. 1 13/24

4. 1 1/4

5. 25/32

6. 3 11/16

7. 1 9/64

Practice Problems Answer Key

8. 1 29/32

9. 4 1/8

10. 14

11. 24 27/32

12. 1 3/64

13. 38 1/4

14. 1 3/64

15. 3 3/16

Good or bad design?

Subtracting Fractions

▪ All denominators must be the same

▪ Find the LCD (least common denominator)

▪ Subtract the numerators and retain common

denominator

▪ Convert to a mixed number

Subtracting Fractions

▪ Example:

▪ What is the least common denominator?

• Change 3/4 so the denominator is 16

=− 16

3 =

Subtracting Fractions

▪ Example:

▪ Subtract numerators and retain the common

denominator

=− 16

12 =−

Subtracting Fractions

Take 15 minutes to complete the

Practice Problems in the textbook.

Practice Problems Answer Key

1. 1/8

2. 7/16

3. 1 1/16

4. 2 15/16

5. 3 9/32

6. 2 5/8

7. 3 9/16

8. 1 3/16

9. 9 53/64

10. 10 1/8

Good or bad design?

Multiplying Fractions

▪ Change all mixed numbers to improper

fractions

▪ Multiply all the numerators

▪ Multiply all the denominators

▪ Reduce to the lowest terms

Multiplying Fractions

▪ Example:

▪ Change all mixed numbers to improper

fractions

= 4 8

1 3

= 1

Multiplying Fractions

▪ Example:

▪ Multiply all the numerators and then the

denominators to get the answer

= 1

100

1 =

Multiplying Fractions

▪ Example:

▪ Reduce the fraction to the lowest terms

100

1 =

1 6

4 6

100 ==

Multiplying Fractions

Take 15 minutes to complete the

Practice Problems in the textbook.

Practice Problems Answer Key

1. 3/8

2. 21/32

3. 4 3/8

4. 2 1/4

5. 6 1/4

6. 19/64

7. 12

8. 4 13/16

9. 8

10. 28

Good or bad design?

Dividing Fractions

▪ Change all mixed numbers to improper

fractions

▪ Invert (turn upside down) the divisor and

multiply

Dividing Fractions

▪ Example:

▪ Change all mixed numbers to improper

fractions

= 2

1 1

1 5

= 2

Dividing Fractions

▪ Example:

▪ Invert the divisor and multiply

1 3

21 ==

= 2

Dividing Fractions

Take 15 minutes to complete the

Practice Problems in the textbook.

Practice Problems Answer Key

1. 11/24

2. 16

3. 8 1/16

4. 26

5. 13/16

6. 2

7. 12

8. 6 18/25

9. 14

10. 1 13/16

Good or bad design?

Calculating Dimensions

▪ Dimensions are made up of whole numbers and

fractions

▪ When adding or subtracting dimensions, inch

and foot values are added or subtracted

separately, beginning with the inch values

• Example: Subtract 9-1 from 12-3

12-3

-9-1

3-2

12-3

-9-1

Decimal Foot Values

(Goodheart-Willcox Publisher)

Area Measurement

▪ Area

• Area of a floor, walls

• Square feet, yards, meters

▪ Length  Width

▪ Use same units of measure

Area:

Square and Rectangular

▪ Example:

• Find the area of a room

that is 76 by 12-5

▪ Solution:

= 52167 2in 324,1191467 =

2ft 64.78144324,11 =

76

12-5

Area:

Square and Rectangular

▪ For lengths given in feet and inches, convert to

decimal feet so the answer is in square feet

▪ Example:

▪ Converted to decimal feet:

= 601321

2ft 625.1285.1052.12 =

Good or bad design?

Triangular Area

▪ Multiply the base times the height

▪ Divide the sum by 2

▪ Example:

5

42 

ft 602120

ft 120425

=

=

Circular Components

▪ Circumference is the distance around a circle

▪ Diameter is the length of a line that bisects the

circle

▪ Radius is half the length of the diameter

▪ Pi () is used to determine the circumference,

area, or volume of a circle

▪ Pi is the ratio of the circumference to the

diameter and is equal to 3.1416

Circular Components

(Goodheart-Willcox Publisher)

Circumference

▪ To find the circumference of a circle, use the

following equation:

Circumference =   d (diameter)

▪ Example:

• Find the circumference of a circle

that is 6-6 in diameter

2ft 42.205.614.3

5.6

=

=

Circumference

▪ Individual portions along the circumference of a

circle are called arcs

▪ Example:

• Determine the length of an arc that has a radius

of 4-3 and an arc of 90

• First, determine the circumference

• Next, determine the portion of the arc

• Then, divide the circumference by the

determined portion of the arc

Circumference

▪ Circumference:

▪ Portion of arc:

▪ Circumference divided by portion:

70.26)225.4( =

25% or 490360 =

86 or 86.647.26 =

Circular Area

▪ To find the area of a circle, use the following

equation: Area=   r2

▪ Example:

• Determine the area of a patio that has a

diameter of 30

ft 86.706A

22514.3A

)1515(14.3A

15A

=

=

=

Good or bad design?

Volume Measurement

▪ Volume is a cubic measure determined by multiplying area

by depth

▪ Example:

• Find the volume of concrete for a 4 thick patio that has

an area of 706.86 ft2

• Convert inches to decimal feet and multiply the area by

the depth:

• Convert the result to cubic yards:

333.0124 = 3

ft 38.235333.086.706 =

3 yd 71.82738.235 =

Activity 2-1: Problems in

Construction Mathematics

Take 30 to 40 minutes to complete

Activity 2-1 in the textbook.